$$100\frac{1}{9}\div66\frac{2}{3}$$
$\frac{901}{600}\approx 1.501666667$
$$\frac{\left(100\times 9+1\right)\times 3}{9\left(66\times 3+2\right)}$$
$$\frac{1+9\times 100}{3\left(2+3\times 66\right)}$$
$$\frac{1+900}{3\left(2+3\times 66\right)}$$
$$\frac{901}{3\left(2+3\times 66\right)}$$
$$\frac{901}{3\left(2+198\right)}$$
$$\frac{901}{3\times 200}$$
$$\frac{901}{600}$$
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$\frac{17 \cdot 53}{2 ^ {3} \cdot 3 \cdot 5 ^ {2}} = 1\frac{301}{600} = 1.5016666666666667$
